My sister is already a US citizen and she can already petition my parents. However, I believe that affidavit of support is required for petitioning a relative. She is willing to petition and requires that my parent should take on a personal health insurance until they become a US citizen plus to give her a durable power of attorney on an existing property to cover for their expense in case of emergency. Is she liable to the extent that she can lose her house to pay for the medical bills in case something happened to them while they are still permanent residents? Is there another way to avoid the power of attorney as this may result in losing the property without the real need of selling it (to mortgage the house for personal gain).

She's misunderstanding the Affidavit of Support. It does not make her liable to pay for their bills or debts or anything like that at all. The only thing is that if they use need-based government assistance, like Medicaid, then the government can ask her for the money used.

As long as the parents do not apply for need-based government assistance, they could rack up millions in private doctor bills, whatever, and it will not affect your sister. The point of the Affidavit of Support is that your sister ensures they have a minimal level of income (it's a very low level, 125% of poverty level), providing additional income if they themselves don't have enough, so that they don't qualify for need-based government assistance in the first place. So as long as she ensures they have this low level of income, she cannot be on the hook for anything.

Plus, very few governments in the U.S. have ever sued sponsors for money used, even when the immigrants have used need-based government assistance.